evaluating the utility of driving: toward automated

354 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012

Evaluating the Utility of Driving: Toward AutomatedDecision Making Under Uncertainty

Robin Schubert, Member, IEEE

Abstract—The complexity of advanced driver-assistance sys-tems (ADASs) is steadily increasing. While the first applicationswere based on mere warnings, current systems actively intervenein the driving process. Due to this development, such systemshave to automatically choose between different action alternatives.From an algorithmic point of view, this requires automatic de-cision making on the basis of uncertain data. In this paper, theapplication of decision networks for this problem is proposed. It isdemonstrated how this approach facilitates automatic maneuverdecisions in a prototypical lane change assistance system. Further-more, relevant research questions and unsolved problems relatedto this topic are identified.

Index Terms—Decision network, decision support system, intel-ligent vehicles, lane change assistant.

I. INTRODUCTION

ONE OF THE main research goals in the domain of intel-ligent transportation systems is to make traveling safer,

more efficient, and more sustainable. Concerning road traffic,advanced driver assistance systems (ADASs), which perceivethe environment of a vehicle using an application-dependentset of sensors, are a promising development toward this aim. Ithas been shown that such systems are indeed having a positiveinfluence on road safety [1].

Over the past few years, a significant increase in complexitycould be observed in the domain of ADASs. While early sys-tems (e.g., blind spot monitoring [2]) restricted themselves tothe provision of warnings, later developments are actively exe-cuting certain maneuvers, such as braking [3]. Current researchprojects are working on even more sophisticated concepts suchas highly automated driving [4] or autonomous vehicles [5].

A common requirement for all these systems is that, at theend of the data-processing chain, a decision needs to be taken.In the simplest case, this decision can be binary (e.g., displaya warning or not), and the procedure for its derivation may bebased on a simple threshold comparison of a certain situationparameter, such as the time to collision. However, there areseveral reasons the process of automatically taking a decisionis becoming significantly more complex for current and, inparticular, future systems.

Manuscript received May 31, 2011; revised August 20, 2011; acceptedSeptember 30, 2011. Date of publication November 4, 2011; date of currentversion March 5, 2012. The Associate Editor for this paper was S. S. Nedevschi.

The author is with Chemnitz University of Technology, 09126 Chemnitz,Germany (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITS.2011.2171952

First, the number of action alternatives is increasing. Whilethe simplest warning-based systems have to choose from onlytwo possibilities, intervention-based functions have, for in-stance, to decide if they need to warn the driver, execute apartial or a full braking maneuver, or are not required to doanything. Highly automated or autonomous vehicles even haveto select the optimal maneuver from a set of given possibilitiessuch as changing the lane, overtaking another vehicle, andstopping. In addition to these discrete decision alternatives,future vehicles can also be expected to decide on continu-ous quantities, e.g., which deceleration to apply to avoid acollision.

Furthermore, the number of decision criteria is also increas-ing. Instead of relying on a single quantity such as the timeto collision, maneuver decisions have to be based on differentaspects such as road safety, passenger comfort, traffic rules, and(in case of cooperative systems) maybe the actions of othertraffic participants as well. Another reason for the increasingcomplexity is the severity of possible consequences, which mayarise from inappropriate decisions. Automatically executing abraking or lane-changing maneuver carries the risk of seri-ous injuries or even deadly incidents. Thus, the validation ofdecision-taking procedures must be further refined.

The probably most critical issue for decision systems is,however, the presence of uncertainty. Due to the limited sensorperformance, a vehicle will never have unequivocal knowledgeabout its surrounding. Even if such knowledge were available,the limited predictability of the traffic situation would stillintroduce significant ambiguities. This uncertainty is increasingwith the earliness of a decision: On the one hand, this is becausethe distance to detected entities is larger, which, in the commoncase of angular sensor errors, results in a more uncertain lateralposition; on the other hand, this results because the time intervalfor predicting the traffic scene is increasing.

Due to these reasons, future intelligent vehicles require reli-able systems for automatically taking decisions that are capableof taking into account several alternatives and multiple criteriain the presence of significant uncertainties. This paper attemptsto propose a potential path toward this aim.

In Section II, a brief summary of current algorithms fordecision taking is given to motivate the work described there-after. Section III introduces decision networks (DNs) as analgorithmic Bayesian framework, which, in theory, complieswith all of the aforementioned requirements. A prototypical im-plementation of DNs on the example of a lane change assistant(LCA) is described in Section IV. The aim of this prototype isto determine a lane-change maneuver recommendation, whichis provided to the driver via a human–machine interface (HMI).

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SCHUBERT: EVALUATING UTILITY OF DRIVING: TOWARD AUTOMATED DECISION MAKING UNDER UNCERTAINTY 355

It will be shown how DNs can be applied as an integral part ofa Bayesian data-processing and data fusion scheme.

In Section V, empirical results of the presented prototype arepresented. In particular, the influence of sensor uncertainties onthe ambiguity of the maneuver decision will be demonstrated.This paper concludes with an analysis of unsolved questionsand further research issues.

II. PREVIOUS WORK ON DECISION ALGORITHMS

As an important aspect for decision algorithms is the ex-istence of appropriate interfaces to previous data-processingsteps, the following overview will be embedded in the contextof the JDL data fusion model:1 This generic model for datafusion is (after having undergone several revision) one of themost widely used schemas for structuring data-fusion-relatedfunctions. In this work, the revised model presented in [6]is applied. The fusion levels 0 (subobject assessment) and4 (process refinement) are not described, as they are not thefocus of this paper. It appears important to emphasize that theselevels do not specify a process model, that is, they do notnecessarily have to be successively performed.

A. Object Assessment

JDL data fusion level 1 is defined as the “estimation andprediction of entity states on the basis of inference from obser-vations” [6]. In most ADAS applications, this means to estimatethe existence, position, and kinematic parameters of differenttraffic participants, as well as the parameters of other relevantentities such as lanes. For that, Bayesian filtering algorithms arepredominant. The main tasks when implementing an ADAS areto choose an appropriate implementation of Bayes’ filter andto design statistical models for the system dynamics, sensors,clutter, etc. If the data fusion levels are separately implemented,the output of the object assessment stage is often a set ofprobability density functions (PDFs) over the relevant entitystates [7].

B. Situation Assessment

JDL level 2 refers to the “estimation and prediction of entitystates on the basis of inferred relations among entities” [6]. Thedifference to level 1 is that, instead of separately analyzingdifferent entities, the relations among them are investigatedto derive a model of the current situation. For ADASs, thismay mean to associate vehicles to certain lanes or to evaluaterelations between vehicles and pedestrians.

Compared to object assessment, the algorithmic variety atthis level is higher. One common approach (particularly for sys-tems with a high computational complexity or low computingresources) is to use the expectation values of the PDFs providedby the previous stage to calculate certain situation parameterssuch as the time to collision [3].

As an alternative, fuzzy-based algorithms are proposed bysome authors to model uncertainty [8], [9]. A situation assess-

1The name of this model is derived from the U.S. Joint Directors ofLaboratories Data Fusion Group, which proposed it in 1985.

ment can then be performed by applying fuzzy rules. One ofthe main drawbacks of this approach is the unavailability ofinterfaces to Bayesian object assessment techniques.

Bayesian techniques for situation assessment are, for in-stance, proposed in [10]. Furthermore, the author proposed aunified Bayesian approach for object and situation assessment,which includes a generic interface between Bayes’ filters andBayesian networks (BNs), as well as an algorithm for exploitingsituational knowledge at the object assessment stage [11].

C. Impact Assessment

The third level of the JDL data fusion model contains the“estimation and prediction of effects on situations of plannedor estimated/predicted actions by the participants” [6]. Thisstage can be seen from two perspectives: On the one hand, itincludes an explicit prediction of maneuvers that are expectedto be performed by the host vehicle or other traffic participants.Although this is an important research questions, it is not thescope of this paper. (Further information and references can,for instance, be found in [12].)

On the other hand, this stage includes the planning of actionsto be executed by the host vehicle. In the context of ADASs,there are two main perspectives on this topic: If actions areplanned on a kinematic level, the term motion planning isusually used. As this concept is well known in robotics, there isa considerable number of approaches (see [13] for a thoroughintroduction on this topic). An application of motion planningto autonomous driving in the context of the DARPA UrbanChallenge is, for instance, given in [14]. The main character-istics of this approach are the optimization of an optimalitycriterion (in this example, the time for following the plannedpath is used) taken into account various restricting constraints.

An alternative perspective is focusing on the high-level be-havior of the host vehicle. From this point of view (whichis taken throughout this paper), impact assessment can beinterpreted as taking maneuver decisions. From an algorithmicperspective, it is (apart from reliability aspects) not relevant ifthe selected maneuver is recommended to the driver or automat-ically executed using a subsequent path-planning module. Therationale of planning on maneuver level is to reduce complexity,as motion planning can be specifically designed for particularmaneuvers.

In the domain of autonomous driving, such an approachhas, for instance, been chosen by different participants ofthe DARPA Urban Challenge. In [15], which illustrates therelationship to different design paradigms from robotics, thisapproach is called behavioral programming. In this work andin [16], decisions are taken using a hierarchical finite-state ma-chine, whereas the state transitions are based on the underlyingdecision rules and the perception results. A similar approach isproposed in [17] in the context of the German project Stadtpilotfor autonomous driving in urban areas. All these works havein common that uncertainties are mainly accounted for on theobject and situation assessment level but not for the decisionprocess itself. In a recent paper about autonomous driving,a multiple-criteria decision-making approach is presented [5].The authors proposed to divide the decision process into two


stages: while the first one determines feasible maneuvers basedon Petri nets, the second selects the most appropriate maneu-ver using a multivariate utility function. While this approachcomplies with the requirements of having different decisionalternatives and multiple criteria, uncertainties are not explicitlyconsidered.

In addition to these methods, there is a variety of algorithmicparadigms for decision taking: Some authors propose to takedecisions based on a set of rules while accounting for uncer-tainties by means of fuzzy theory. Such an approach for takingmaneuver decisions is, for instance, proposed in [18] and [19].Alternatively, sensor uncertainties are modeled by intervals toinfluence the decision [20]. In [21], a human-centered decisionapproach is proposed. The authors argue that decisions that arebased on one optimality criterion are not suitable for appli-cations that involve technical systems and humans. Comparedwith the argumentation in Section I, the requirement to have atradeoff between safety and comfort aspects can be interpretedas decision taking based on multiple criteria.

A statistical approach for decision making is presentedin [22]. This approach is based on an acceleration-based metricand models the binary decision process as a hypothesis test.This problem is solved using Monte Carlo integration, whichappears interesting due to the natural interface toward MonteCarlo techniques for object assessment.

It turns out that decision algorithms that can handle anarbitrary number of alternatives and multiple decision criteriain the presence of uncertainty and facilitate a natural connectionto the object and situation assessment stage are rarely available,although numerous sophisticated systems that focus on a subsetof these requirements have been proposed.

From a Bayesian point of view, it appears natural to applyDNs to this problem. As it will be shown in the following sec-tion, this framework complies with the defined requirements,although there are nevertheless several practical issues to solve.The application of DNs to a prototypical ADAS application isdescribed in the remainder of this paper. However, there are alsoauthors that propose alternative representations of uncertainty.A proposal of an evidential network based on belief theory is,for instance, presented in [23]. This work does not attempt tocompare Bayesian and non-Bayesian approaches. The decisionfor a Bayesian approach has been mainly taken due to the pre-dominant usage of Bayesian techniques at the object assessmentlevel, which implies that, by also using the Bayesian paradigmfor situation and impact assessment, a unified approach forhandling uncertainties can be expected.

Due to the complexity of the illustrated system, this workbuilds on two previous publications: In [24], the prototypi-cal implementation of an ADAS for lane change assistanceis presented, including detailed information about the objectassessment stage (e.g., tracking and filtering techniques, aswell as process and sensor models). The content of [11] ismore related to the situation assessment stage. In particular, abidirectional interface between object and situation assessmentis investigated.

The focus of this work is to both complete the previouspublications in terms of impact assessment and present thetopic of decision taking under uncertainty in a more general

context due to its relevance for future ADASs. A unified andsignificantly more detailed presentation of these topics can befound in [25].

III. DECISION NETWORKS

DNs, which are also known as influence diagrams [26], arean extension of BNs for deriving decisions under uncertainty.In the following material, which is based on [11], BNs willbe introduced, followed by a description of the necessaryextensions for DNs.

A. Bayesian Networks

BNs are a graph-theoretic concept for representing un-certain and incomplete knowledge using Bayesian statistics.A BN can be formally defined as a directed acyclic graph(DAG) G = {X , E}, which contains a set of nX nodes X ={X1, . . . , XnX

} and a set of directed edges E = {Xi →Xj |Xi,Xj ∈ X , i �= j} pointing from a parent node to a childnode. The set of all parent nodes of Xi is denoted by Pa(Xi).All nodes Xk for which a path exists from Xi to Xk, that is,there is a sequence of nodes [Xi, . . . , Xk] such that (Xj−1 →Xj) ∈ E ∀j ∈ [i + 1, . . . , k], are called descendants of Xi.Likewise, all nodes Xk for which a path exists from Xk to Xi

are referred to as ancestors of Xi [27].Each node in a BN represents a random variable that can

either be discrete or continuous. Each edge denotes a direct con-ditional dependence relationship between two nodes, which isquantified by a conditional probability table (CPT) representingthe conditional probability distribution P (Xi|Pa(Xi)). Usually,the direction of the edge represents a causal relationship; that is,edges are drawn from cause nodes to effect nodes.

A BN can be interpreted as a factorized representation ofa joint probability distribution. In fact, each joint distribu-tion can be written in an alternative form using the chainrule, which can be derived from the definition of conditionalprobability

P (X1, . . . , XnX) =

nX∏

i=1

P (Xi|Xi−1, . . . , X1). (1)

For i = 1, the factor is the unconditional probability P (X1).It follows from this identity that the DAG G previously

defined is a BN if and only if the joint probability distributionof the random variables represented by X can be factorized asfollows:

P (X1, . . . , XnX) =

nX∏

i=1

P (Xi|Pa(Xi)) . (2)

This definition implies that, for each random variable in thenetwork

P (Xi|Xi−1, . . . , X1) = P (Xi|Pa(Xi)) (3)

holds, that is, each variable is conditionally independent fromits nondescendants, given the values of its parent variables. Thisis sometimes also called the local Markov property.


The main advantage of BNs, compared with other represen-tations of joint probability distributions, is the possibility tomodel conditional independence, which drastically decreasesthe number of necessary conditional probabilities. Furthermore,graphical modeling makes it easier for a human designer toadapt the model to his or her perception of the system char-acteristics. At the same time, the concept of BNs is formalizedenough to allow efficient computational evaluation.

The most important task for BNs is the ability to performprobabilistic reasoning. That is, knowledge about the stateof certain nodes (which is generally called evidence) can beincorporated into the network for the purpose of calculatingthe joint probability distribution p(X1, . . . , XnX

|e) of the othernodes under the condition of the entered evidence e. While,for small networks, the reasoning can be done in a simple wayusing enumeration, efficient algorithms exist to allow real-timeoperations for larger models (see, for instance, [28]).

B. Decision and Utility Nodes

DNs are extending the syntax of BNs by introducing twoadditional types of nodes. To avoid ambiguities, the nodes thathave been used in the previous section (representing randomvariables) are henceforward called chance nodes. The othertypes are decision nodes and utility nodes.

1) Decision nodes represent occasions where the decisionmaker has to choose between a set of discrete alternatives.Each alternative is reflected by one particular state ofthe node. Edges pointing from decision nodes to chancenodes indicate a direct dependency between the deci-sion and those variables. Conversely, the interpretation isslightly different: Edges pointing to decision nodes arecalled information links and indicate that the state of theparent is known prior to the decision [26].

2) Utility nodes represent the utility function of the decisionmaker. A utility function can be defined as a mappingfrom the state space to real numbers [27]—given that thedecisions are part of the state space. Usually, normalizedutilities, which assess the best possible outcome by unityand the worst state by zero, are used. The parents ofa utility node comprise all chance and decision nodesthat directly affect the utility. The utility function itselfis often represented by a conditional utility table (CUT)in similarity to the CPTs.

According to [26], a DN is a DAG consisting of chancenodes, decision nodes, and utility nodes with the followingproperties.

1) There is a directed path comprising all decision nodes.2) Utility nodes do not have children or states.3) Decision nodes have a finite set of mutually exclusive

states, which represent decision alternatives.4) A conditional probability distribution P (Xi|Pa(Xi)) (en-

coded in a CPT) is associated to each chance node Xi.5) A real-valued function U(Ui|Pa(Ui)) is associated to

each utility node Ui.

DNs can be solved by applying the maximum expected utility(EU) principle, that is, the decision alternative with the highest

EU is chosen. To determine the EU values, the posterior proba-bility distribution for the parents of the utility node needs to becalculated for each possible decision alternative—conditionedon every available piece of evidence. If the decision node isset to one particular state, it behaves like a chance node thatreceived hard evidence; that is, any inference algorithm for BNscan be applied. The required EU can then be calculated using

EU(Xd|e) =∑

x∈Pa(U)

P (x|Xd, e)U(x) (4)

where Xd denotes the decision node, x represents all possiblestate permutations of Pa(U), and U(x) is the utility value for acertain instantiation of U ’s parent nodes.

C. Advantages and Limitations

DNs are based on a sound theoretical foundation; that is, alloperations in these networks are derived from the three axiomsof probability. In addition, the design of DNs can be decom-posed into a structural and a quantitative part. The structuremainly captures causal and independence relationships, whichare considered easier to construct than full probabilistic mod-els. The necessity of deriving numerous CPTs is occasionallycriticized in literature (e.g., in [29]). However, provided that asufficient amount of data is available, these parameters can alsobe automatically learned [26].

Due to the exploitation of conditional independence rela-tionships, BNs are computationally tractable for many practicalapplications. Limitations exist for complex hybrid models anddynamic DNs. Furthermore, there is a close similarity betweenDNs and the Bayes’ filter, which is prevailingly used fortracking purposes. As it is demonstrated in [11], this facili-tates close interactions between tracking, situation, and impactassessment.

Compared with the requirements derived in Section I, it turnsout that DNs are capable of dealing with numerous decision al-ternatives. This can be achieved by having an arbitrary numberof states within one decision node or even by modeling severaldecision nodes. The latter approach also facilitates decisionsequences.

DNs can naturally handle uncertainties, which may arisefrom both uncertain evidence or the situational model itself. Ifthe adaptive likelihood nodes proposed in [11] are used, sensoruncertainties can directly influence the final decision.

In addition, multiple decision criteria can theoretically beincorporated into a DN. One possibility is to use several utilitynodes, which results in the inference algorithm maximizing thesum of all EUs. Another possibility is to use multiple decisioncriteria but still blend them into one utility function. However,as the next section is going to demonstrate, the availability ofpractical guidelines for constructing such utility functions iscurrently not satisfying, which can be considered as the mainlimitation of DNs at the moment.

Another limitation for DNs is the disability to efficientlyhandle arbitrary continuous distributions. Even if Gaussianrepresentations are applied, many exact inference techniquescannot be applied.


Fig. 1. Sensor configuration of the maneuver recommendation system.

IV. IMPLEMENTATION IN A LANE-CHANGE ASSISTANT

The algorithms proposed in this paper are illustrated on theexample of a system that is capable of assessing the currenttraffic situation on highways to give lateral maneuver recom-mendations to the driver. The recommendation may advice thedriver to stay on the current lane or to perform a lane-changemaneuver (either left or right). In the following, the systemarchitecture and the algorithmic principles of the object andsituation assessment stages will be presented based on twoprevious publications by the author [11], [24]. After that, theapplied DN will be described.

A. System Architecture

Fig. 1 shows the sensor configuration of the system. A77-GHz long-range radar in the driving direction and two24-GHz medium-range radars in the opposite direction aredetecting vehicles in the environment of the ego vehicle. Thisperception task is supported by two grayscale cameras (one ineach direction), which are also used for detecting lane markingson the road surface. Additionally, ego motion data from the egovehicle controller-area-network bus are used.2

The modular functional structure of the system is shown inFig. 2. Each lane estimation module provides a Gaussian PDFover the state-variable curvature, distortion, lateral offset, andlane width. In addition to those geometric properties, the laneestimation modules also perform a discrimination analysis ofthe lane borders into the classes continuous, noncontinuous, andnoise. This analysis is based on the frequency power spectrumof the lane detections [30]. As dashed- or solid-lane borders inmany countries represent a permission or a prohibition of lane-change maneuvers, respectively, this information is used as aninput for determining the maneuver recommendation.

The two vehicle-tracking modules are estimating the exis-tence, position, and dynamic parameters of all detected objectsusing unscented Kalman filters [31]. The motion of the vehiclesis modeled using a Constant Turn Rate & Acceleration motionmodel [32]. The output of the modules is a Gaussian PDFover the state-variable position, heading, velocity, yaw rate,and acceleration for each object whose existence probabilityexceeds a predefined threshold.

2It can be noted that the sensor configuration of the prototype contains asignificant blind spot area, which makes it impossible to detect vehicles besidethe host vehicle. While this is obviously critical for an end-user implementation,this restriction could (under controlled test conditions) be compensated bypredicting vehicles that have been previously detected by the sensors whilethey are located in the blind spot zone. More details about this approach canbe found in [24].

B. Probabilistic Situation Assessment

To derive a lateral maneuver recommendation, different sit-uation variables need to be determined from the perceptionresults. In the proposed system, those situation variables arerepresented by chance nodes of a DN, which are described inthe following.

1) BorderLeft/BorderRight: These two nodes denote thelane border type, which can be either Continuous orNoncontinuous.

2) EgoLane/LaneLeft/LaneRight: These three variables de-scribe the status of the lane under consideration withrespect to its occupancy. The possible states are Free(that is, there are no vehicles within a relevant dis-tance), Occupied (the closest vehicle in the lane iswithin a relevant distance but outside a critical distance),and Dangerous (the closest vehicle is inside the safetymargin).

3) LaneChangeLeft/LaneChangeRight: These nodes de-scribe the feasibility of a lane change maneuver to theleft or to the right. State Impossible indicates that sucha maneuver is by no means to be performed because itis either not safe or not allowed. In contrast, state Safedeclares that the maneuver is allowed and that there isno relevant vehicle in the target lane. However, a highprobability of this state does not necessarily mean that themaneuver is recommended—this is evaluated in a sepa-rate decision node. The third state Possible representssituations in which a lane change is allowed, but there is avehicle present in the target lane at a noncritical distance.

The interface between the DN and the unscented Kalmanfilters used at the object assessment stage is based on theconcept of adaptive likelihood nodes proposed in [11]. In thisapproach, particular likelihood functions are designed for thethree nodes, which represent the occupancy of the lane. Theselikelihood functions implicitly cover the aspects of associatingvehicles to lanes and determining if a vehicle is within a criticalsafety margin.

The DN does not contain any temporal interdependencies,that is, the situations and decisions are not directly dependenton previous situations or decision, respectively. The rationalebehind this approach is that temporal dependencies are exces-sively applied at the object assessment level. Adding additionaltemporal relationships would decrease the modularity of thesystem and increase the required resources for validation.

C. Deriving Maneuver Decisions

The ultimate goal of the DN described in the previous sectionis to derive lane-change maneuver decisions. As previouslydescribed, this can be achieved by adding decision and utilitynodes. For the LCA, there are three possible maneuvers thatare represented by the decision node LateralManeuver (LM):The host vehicle may stay on the current lane (state KL =KeepLane) and perform a lane change maneuver to the left(CL) or right (CR).

To derive a decision, each alternative needs to be evaluatedwith respect to a utility value, where a high utility represents


Fig. 2. Functional structure of the maneuver recommendation system.

Fig. 3. DN for deriving lane change maneuver decision. In contrast to a BN, this graph also contains utility node S and decision node LM. If no evidence isavailable, the illustrated prior probability distribution leads to the recommendation of the maneuver KeepLane. The EUs for CL and CR are not symmetrical asa lane change to the left is recommended in more situations than one to the right. The interface between the lane occupancy nodes and the object assessmentstage is implemented by calculating PDFs for two situation variables called normalized lateral position and DST for each vehicle and combining them usinga combinatorial relation [11]. For determining probability distributions over these quantities, the PDFs of the lane and the vehicles are used as inputs for theUnscented transform.

a more desirable situation than a lower one. For the LCA, themain requirement is that, regardless of the chosen maneuver,the host vehicle remains safe. Thus, the utility node in thissystem is called Safety (S). The complete network is shownin Fig. 3.

The main effort in designing a DN is to define the CUT.This table must contain a utility for each possible combinationof the situation variables and the decision alternatives; that is,

U(S|LM, LCL, LCR, EL).3 In other words, the utility depends onthe current situation and the decision, which is also representedby the fact that all edges point toward S. The complete list ofconditional utilities is given in Table I.

3This motivates the introduction of nodes LCL and LCR, which are notnecessary from a functional point of view. However, these nodes reduce thesize of the CUT from 22 · 34 = 324 to 34 = 81.


TABLE ICUT FOR NODE S, WHICH REPRESENTS A QUANTIFICATION OF THE UTILITY FOR EACH POSSIBLE COMBINATION OF SITUATION AND DECISION

It does not appear reasonable to give a detailed explanation ofeach row in the table. Instead, particular properties and selectedsituations shall be explained in the following.

As a first observation, it may be noted that the utilities areeither zero or unity. In other words, a maneuver is regarded aseither safe or unsafe, without intermediate values. Furthermore,there is only one unity entry in each row of the table, whichimplies that, for each situation, there is exactly one nominalmaneuver. These properties are no general requirements forutility values. For the LCA, they have been chosen to avoida continuous quantification of the parameter Safety. In fact,this parameter determines if a maneuver possibly leads to anaccident, which may cause severe injuries or even loss of lives.For this reason, a rather rigorous interpretation of the safetyvalue has been applied, instead of defining which situations are“slightly safer” than others.

A particular tribute to the German traffic regulations isrepresented by the three unity values for the maneuver CR. OnGerman roads outside towns with several lanes per direction,there is an obligation to use the rightmost lane, unless thevehicle is overtaking another traffic participant. Furthermore,another vehicle may only be overtaken on its left side. Thisis implemented in a rather restricted way by the LCA. Onlyif a lane change maneuver to the right is considered safe andthere is no relevant vehicle on the ego lane is this maneuverrecommended. The motivation behind this design decision isthat, if the ego lane is occupied, there is a significant prob-ability that the host vehicle is going to overtake the vehicleahead.

As a lane change maneuver is potentially dangerous, thenumber of situations where it is recommended is kept to aminimum. This is reflected by the fact that there are only six

entries in Table I that recommend a lane change maneuver to theleft. In fact, such a maneuver is only recommended if LCL = S(that is, if the maneuver is considered as safe) and if the egolane is not free. This design is also due to the primacy of safety.In reality, lane change maneuvers are often performed if theneighbor lane is occupied, provided that the vehicle ahead isoutside the safety margin. However, for the LCA, a conservativeimplementation has been chosen, which recommends keepingthe lane unless the left neighbor lane is indeed completelyfree.

The proposed CUT has been designed for a lane-changeassistant, which is considered to be a comfort system. Thus,lane changes are not recommended to avoid collisions. In fact, ithas been assumed during the design that additional longitudinalcontrol takes place (by either the driver or, for instance, an addi-tional adaptive cruise control system). This is the reason why, inTable I, it is not distinguished between the states Occupied andDangerous of the ego lane. However, the definition of these twostates facilitates the extension of the decision module to lateraland longitudinal maneuvers.

D. Maximum EU Decision and Ambiguity Measure

Taking a decision means to calculate the expectation valueof the utility for each decision alternative, i.e., the EU, con-ditioned on the available evidence. Thus, the final decision isgiven by

LM∗ = maxm∈LM

EU(m). (5)

To obtain an ambiguity measure of the decision, the authorproposes to calculate a value that is similar to the normalized


Fig. 4. Images of the (top row) front camera and (bottom row) rear camera during the field test scenario. The result of the lane recognition module is illustratedby the yellow curves. The four columns correspond to the times t = 4.7 s, t = 9 s, t = 18.5 s, and t = 20.7 s.

entropy for probability distributions, i.e.,

H = −∑

m∈LM

EU(m)log2 EU(m)log2 |LM|

(6)

where |LM| denotes the number of decision alternatives. In ac-cordance with the standard properties of entropy, the definition

limEU(m)→0

EU(m) log2 EU(m) = 0 (7)

holds to allow a calculation, even if one EU is zero.If H = 1, the EUs are uniformly distributed, and the ambi-

guity of the obtained decision is high. On the other hand, ifH = 0, one decision alternative yields an EU of unity, whereasthe others yield zero. In this case, the decision can be acceptedwith high confidence. Thus, the quantity H may serve as anambiguity measure for the derived decision, and each applica-tion may define a threshold that has to be exceeded to accept adecision. It appears relevant to emphasize that the calculationof H does, by no means, increase the amount of availableinformation; however, it may serve as a useful quantity forapplication designers who have a preference for an uncertaintymeasure encoded in one single number.

V. EMPIRICAL RESULTS

For the evaluation, a scenario was selected from recorded testdata, which contains an exemplary overtaking maneuver. Thescene has a duration of approximately 22.5 s and is shown inFig. 4.

During the scene, the host vehicle is traveling on a partof a two-lane highway, on which lane-change maneuvers areallowed by traffic regulations. The environment of the hostvehicle consists of one additional vehicle, which is travelingon the right lane of the highway in front of the host vehicle atthe beginning of the scene. As the host vehicle approaches theobject, it performs a lane change maneuver to the left, passesthe vehicle, and returns to the right lane. The lane changes takeplace at t = 4.6 s and t = 20.6 s.

A particularity of the prototype is the existence of a blindspot area that is not covered by any sensor. In the evaluated

scenario, the tracked object is outside the sensors’ fields ofview (FOVs) between t = 5.5 s and t = 15.5 s. To demonstratethe consequences of this limitation, the uncertainty of theobject’s longitudinal position ox is also shown in Fig. 5(a) bymeans of a 3σ-confidence interval. It can be observed that,during the blind spot period, this uncertainty is significantlyincreasing.

Fig. 4 also shows the results of the subobject and objectassessment stages: The yellow curves visualize the estimatedlane parameters. In addition, the front images also show thediscrimination analysis of the lane markings, which correctlymarks the center line as noncontinuous and the road bordermarkings as continuous. Objects whose existence probabilitiesexceed a certain threshold are denoted by elliptic overlays inthe camera images of Fig. 4. The colors of these overlayscorrespond to the result of the individual threat assessment:Green and yellow ellipses represent the states Free and Occu-pied, whereas red indicates that the object is evaluated as beingDangerous.

Fig. 5(b) shows the EU of each decision alternative: Atthe beginning of the scene (until t < 4.6 s), the EU for KLis decreasing, whereas the EU of state CL is increasing. Thisresults from the shrinking distance to the tracked object, whichleads to the ego lane’s occupancy slowly changing from Freeto Occupied. A particularity occurs at t = 4.6 s: As the hostvehicle is crossing the lane border, the left lane, which waspreviously considered to be a neighbor lane, is now interpretedas the ego lane. Conversely, the lane that was regarded as beingthe ego lane before the lane change is considered as the rightneighbor lane afterward. As a consequence, the EU for a lanechange to the left is dropping due to the continuous road border,whereas the EU for KL is increasing.

While the object is located in the host vehicle’s blind spotzone (between t = 5.5 s and t = 15.5 s), the ambiguity ofthe EU distribution is significantly increasing. This reflectsthe direct influence of the uncertainties, which result from theobject assessment stage on the maneuver decision.

At t = 19.4 s, the host vehicle is leaving the safety marginof the object. In accordance to German traffic regulations, alane change maneuver to the right is immediately becoming themaneuver with the highest EU. Finally, as the host vehicle is


Fig. 5. Results of LCA during the exemplary overtaking scene illustrated in Fig. 4. (a) The offset of the lane border (dashed/red) and the longitudinal distance tothe tracked object (solid/blue) are shown. The gray area denotes the 3σ-confidence interval for ox, which is increasing due to the blind spot zone. (b) The expectedmaneuver utilities for the field test scenario are changing while the host vehicle is approaching. At t = 4.6 s and t = 20.6 s, the expected utilities are swappingdue to the lane changes of the host vehicle. (c) The final maneuver decision and the normalized ambiguity of the maneuver utility distribution. The ambiguity issteadily increasing during the blind spot period, which reflects the growing object assessment uncertainties.

Fig. 6. Images of the (top) front camera and (bottom) rear camera during selected scenes of the field test scenario.

crossing the lane border at t = 20.6 s, the roles of the lanes arechanging again.

The colored bar at the top of Fig. 5(c) shows the final maneu-ver decision, which is obtained according to (5). In addition, theproposed ambiguity value is shown. It can be observed that this

quantity can indeed be interpreted as an uncertainty measure,as it is particularly high in periods where the EU distributionis comparably ambiguous. Furthermore, the effect of the blindspot period is clearly reflected by the steady increase in Hbetween t = 5.5 s and t = 15.5 s.


TABLE IIRESULTS OF THE SITUATION ASSESSMENT FOR SELECTED SCENES. EACH

COLUMN OF THE TABLE CORRESPONDS TO A COLUMN IN FIG. 6

Further to the overtaking scenario, additional selected scenesof the field test trials are shown in Fig. 6. Each row of this figurerepresents a separate scene. The columns of Table II contain allrelevant results of the situation assessment for each of thesescenes.

In the first scene, the ego lane is occupied by an object infront of the host vehicle. The left lane, however, is evaluatedas Free due to the fact that the object behind the host vehicleis traveling slower than the host vehicle and the safety timemargin is not violated. Thus, it is recommended to perform alane change maneuver to the left. The second column of Fig. 6shows the same scene 4 s later. Due to a deceleration of thehost vehicle, it is now traveling slower than the rear object.As a result, the deceleration to safety time (DST) is no longerzero, which, in turn, changes the evaluation of the left laneto Dangerous. Due to this change, the maneuver recommen-dation changes to Keep Lane; however, there is a significantuncertainty for this recommendation, which is reflected by theambiguity value. This behavior illustrates the influence of therelative velocity on the situation assessment result.

The third column shows a rather complex scene with fourobjects in front of the host vehicle and three objects behind it.However, the probability distributions reveal that, despite thishigh number of objects, the situation is much less ambiguousthan the previous situations. In fact, the clear evaluation ofthe right neighbor lane as Dangerous results in an unequivocalrecommendation to keep the current lane. This recommendationis supported by an ambiguity of zero.

The last column of Fig. 6 shows that the prediction of objectsin the blind spot area is also possible if the host vehicle isovertaken, instead of performing an overtaking maneuver itself.In this scene, the object on the left lane in front of the hostvehicle is not within the FOV of the front radar yet.

VI. UNSOLVED ISSUES AND FUTURE RESEARCH

Although the results presented in the previous sectiondemonstrate the potential of DNs for deriving maneuver deci-sions under uncertainty, this proof of concept is, by no means,capable of giving answers to all related questions. Thus, adiscussion about limitations of the presented approach and openresearch questions will be given in the following.

A first observation is that the DN approach rigorously trans-forms uncertainties that are associated to object states intoambiguities of the maneuver decision. Using the proposednormalized ambiguity measure, a threshold may be defined toact only if the confidence is within an acceptable range. As aconsequence, there will be periods in which the system is notcapable of producing a result at all. While this may appearas a limitation from a superficial point of view, the authorprefers to consider this behavior as a strength of the approach,as it appears beneficial to obtain an “honest” error messagefrom the system instead of a potentially unreliable result. Infact, pretending a reliability that cannot be justified due to theambiguity of the current situation appears potentially safetycritical.

However, this does not solve the problem of uncertainty butonly shifts it to another part of the data processing. It needs tobe defined what an intelligent vehicle has to do if it discoversthat it is not capable of providing a clear result, i.e., some kindof fallback action that minimizes the risk of having an accidenton the majority of situations is necessary.

The requirement of having an arbitrary number of decisionalternatives can be easily achieved by adding more states tothe decision node. If the problem can be divided into severaldecisions that can be sequentially taken, a set of separatedecision nodes can be applied.

Taking into account several decision criteria can theoreticallybe achieved by using several utility nodes, each of which mod-els a particular aspect of the decision process (e.g., safety, trafficregulations, and comfort). A weighting of the criteria could beachieved by using different codomains for each utility scale.However, it is difficult to prevent several less-important criteriafrom overriding a particularly important one. An alternativemay be to use only one utility node whose CUT has beenobtained by multiplying the utilities of different decision crite-ria. For instance, it appears reasonable to evaluate the aspectsof safety and compliance to traffic regulations using binaryutilities, i.e., zero or unity. On the other hand, criteria such ascomfort can possibly be defined on a continuous scale. If thesethree utilities are multiplied, unsafe or prohibited alternativesreceive a utility of zero, whereas all others are evaluated withrespect to the driver’s comfort. This discussion illustrates thatthere are numerous open questions related to the constructionof appropriate utility functions.

In other domains, approaches such as Pareto optimizationare applied to multiobjective decision [33]. Even though suchapproaches do not necessarily produce one clear result for eachpossible situation, their application to the ADAS domain mayprove useful to reduce complexity.

Another issue is the complexity of the design process.Even for the relatively simple decision problem presented inthis paper (which assumes that the utility of the decision isinfluenced by only three situation variables with only threestates each) 34 = 81 utility values need to be specified. Thisnumber significantly increases if the situational model becomesmore complex.

An alternative design strategy that is proposed in [5] isto separately evaluate each situation variable, instead of con-sidering each permutation. While this drastically reduces the


design effort, it may introduce problems in the validation of thedecision system.

Finally, the validation of a probabilistic decision system mayalso prove difficult. On the one hand, it needs to be verifiedthat the correct decisions are taken (while correct may beinterpreted in a technical but also in a subjective human-centricway). On the other hand, the validation would have to determineif the confidence value is correct, i.e., if decisions are providedonly if they are certain enough.

Despite these issues, the application of DNs in the ADASdomain appears natural, as they facilitate a unified Bayesianview on the data-processing chain from the sensor to thedecision stage. Furthermore, all requirements that have beendiscussed in the introduction of this paper can be met, whereasthe computational complexity is comparably low. Thus, furtherresearch on this topic appears both necessary and promising tocontinue the development toward safer and more comfortablevehicles.

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Robin Schubert (S’07–M’11) received the Diplomaand the Ph.D. degree in electrical engineering withdistinction from Chemnitz University of Technology,Chemnitz, Germany, in 2006 and 2011, respectively,and the Diploma in business administration fromFernUniversität, Hagen, Germany, in 2010.

He is currently a Research Assistant with Chem-nitz University of Technology, where he is coordi-nating the Data Fusion Research Group with theProfessorship of Communications Engineering. Hisresearch interests include data fusion, probabilistic

filtering, situation assessment, and vehicle localization.Dr. Schubert was the recipient of the Hermann Appel Award in 2011.

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